The present invention relates generally to 2D and 3D computerized tomography (CT). In particular this invention relates to methods and systems for reconstructing projection data which are neither equilinear or equiangular in nature.
In conventional computerized tomography for both medical and industrial applications, an x-ray fan beam and an equilinear or equiangular array detector are employed. Two-dimensional (2D) axial imaging is achieved. While the data set is complete and image quality is correspondingly high, only a single slice of an object is imaged at a time. When a 3D image is acquired, a “stack of slices” approach is employed. Acquiring a 3D data set one slice at a time is inherently slow. Moreover, in medical applications, motion artifacts occur because adjacent slices are not imaged simultaneously. Also, dose utilization is less than optimal, because the distance between slices is typically less than the x-ray collimator aperture, resulting in double exposure to many parts of the body.
In a system employing true cone-beam geometry, a cone-beam x-ray source and a flat 2D equilinear or curved 2D equiangular area detector are employed. An object is scanned, preferably over a 360-degree range, either by moving the x-ray source in a scanning circle around the object while keeping the 2D area detector fixed with reference to the source, or by rotating the object while the source and detector remain stationary. In either case, it is the relative movement between the source and object which affects scanning. Compared to the 2D “stack of slices” approach for 3D imaging, the cone-beam geometry has the potential to achieve rapid 3D imaging of both medical and industrial objects, with improved dose utilization.
The cone-beam geometry for 3D imaging has been discussed extensively in the literature, as represented by the following: M. Schlindwein, “Interactive Three-Dimensional Reconstruction from Twin Cone-Beam Projections”, IEEE Trans Nucl. Sci., Vol. NS-25, No. 5, pp. 1135-1143 (October 1978); Gerald N. Minerbo, “Convolutional Reconstruction from Cone-Beam Projection Data”, IEEE Trans. Nucl. Sci., Vol. NS-26, No. 2, pp. 2682-2684 (April 1979); Heang K. Tuy, “An Inversion Formula for Cone-Beam Reconstruction”, SIAM J. Math, Vol. 43, No. 3, pp. 546-552 (June 1983); L. A. Feldkamp, L.C. Davis, and J. W. Kress, “Practical Cone-Beam Algorithm”, J. Opt. Soc. Am. A., Vol. 1, No. 6, pp. 612-619, (June 1984); Bruce D. Smith, “Image Reconstruction from Cone-Beam Projections: Necessary and Sufficient Conditions and Reconstruction Methods”, IEEE Trans. Med. Imag., Vol. MI-44, pp. 14-24 (March 1985); and Hui Hu, Robert A. Kruger, and Grant T. Gullberg, “Quantitative Cone-Beam Construction”, SPIE Medical Imaging III: Image Processing, Vol. 1092, pp. 492-501 (1989).
Several methods for collecting cone beam data have been developed. One technique involves acquiring volumetric image data using a flat panel matrix image receptor, as described in U.S. Pat. No. 6,041,097 to Roos, et al. Another method uses image intensifier-based fluoroscopic cameras mounted on a CT-gantry type frame. Such a system is described in a paper presented at SPIE Medical Imaging Conference on Feb. 24, 1997, by R. Ning, X. Wang, and D. L. Conover of Univ. of Rochester Medical Center.
U.S. Pat. No. 5,319,693 to Eberhard, et al. discusses simulating a relatively large area detector using a relatively small area detector by either moving the actual area detector relative to the source, or moving the object relative to the detector.
However, there is a significant limitation of cone-beam reconstruction when individual flat detectors are reconstructed independently. Simply combining separate reconstructed portions of the object from independently processed projections results in an image characterized by discontinuous jumps between the various projections. Alternatively, one could first combine the discreet data sets from each detector into a new single data set that is then reconstructed. However, by simply combining the data into a larger data array and performing standard reconstruction techniques, the data elements in the new data set are not equally spaced. Thus, the resultant images will be distorted geometrically, or the dynamic range of the reconstructed data set will not represent the true transmission values of the object being imaged.